Properties

Label 27.9.f
Level $27$
Weight $9$
Character orbit 27.f
Rep. character $\chi_{27}(2,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $138$
Newform subspaces $1$
Sturm bound $27$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 27.f (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(27\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(27, [\chi])\).

Total New Old
Modular forms 150 150 0
Cusp forms 138 138 0
Eisenstein series 12 12 0

Trace form

\( 138 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 447 q^{5} - 774 q^{6} - 6 q^{7} - 9 q^{8} - 12960 q^{9} + O(q^{10}) \) \( 138 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 447 q^{5} - 774 q^{6} - 6 q^{7} - 9 q^{8} - 12960 q^{9} - 3 q^{10} + 28668 q^{11} + 77421 q^{12} - 6 q^{13} - 120975 q^{14} + 105507 q^{15} - 774 q^{16} - 9 q^{17} - 241317 q^{18} - 3 q^{19} + 137913 q^{20} + 1164372 q^{21} - 185478 q^{22} + 68376 q^{23} - 2624256 q^{24} + 507585 q^{25} + 3500568 q^{27} - 12 q^{28} - 943980 q^{29} - 1533627 q^{30} + 920739 q^{31} - 3005136 q^{32} - 1245285 q^{33} + 660474 q^{34} + 6225408 q^{35} + 4021128 q^{36} - 3 q^{37} - 23716884 q^{38} - 5699685 q^{39} - 975273 q^{40} + 16694382 q^{41} + 1594134 q^{42} + 4412514 q^{43} + 17341119 q^{44} + 12986721 q^{45} - 3 q^{46} - 11341869 q^{47} - 26229183 q^{48} + 11347482 q^{49} - 40948977 q^{50} - 16497396 q^{51} + 14465511 q^{52} + 34106454 q^{54} - 12 q^{55} + 52215771 q^{56} + 26766582 q^{57} - 19078611 q^{58} + 76116738 q^{59} - 24031170 q^{60} + 34059450 q^{61} - 223709616 q^{62} - 149069421 q^{63} + 100663293 q^{64} + 20396037 q^{65} + 83336805 q^{66} - 103603884 q^{67} + 101921427 q^{68} + 38038563 q^{69} + 135373629 q^{70} + 125718795 q^{71} + 183269700 q^{72} - 7632642 q^{73} - 66643887 q^{74} - 167459145 q^{75} - 203790342 q^{76} - 343269159 q^{77} - 344470788 q^{78} - 68767890 q^{79} + 151392924 q^{81} - 12 q^{82} + 383244663 q^{83} + 836800692 q^{84} + 170435619 q^{85} + 71426730 q^{86} - 145695735 q^{87} - 192774918 q^{88} + 135692730 q^{89} - 821329020 q^{90} + 77546796 q^{91} - 1343159175 q^{92} - 414573177 q^{93} - 44451609 q^{94} + 881099997 q^{95} + 1578184830 q^{96} + 31339344 q^{97} + 1293135102 q^{98} + 228876057 q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(27, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
27.9.f.a 27.f 27.f $138$ $10.999$ None \(-6\) \(-6\) \(-447\) \(-6\) $\mathrm{SU}(2)[C_{18}]$